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Newton iteration for lexicographic Gröbner bases in two variables (2302.03766v1)
Published 7 Feb 2023 in math.AC, cs.SC, and math.AG
Abstract: We present an $m$-adic Newton iteration with quadratic convergence for lexicographic Gr\"obner basis of zero dimensional ideals in two variables. We rely on a structural result about the syzygies in such a basis due to Conca and Valla, that allowed them to explicitly describe these Gr\"obner bases by affine parameters; our Newton iteration works directly with these parameters.